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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 2 — Feb. 1, 2008
  • pp: 348–356

Regularizing active set method for retrieval of the atmospheric aerosol particle size distribution function

Yanfei Wang and Changchun Yang  »View Author Affiliations

JOSA A, Vol. 25, Issue 2, pp. 348-356 (2008)

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The determination of the aerosol particle size distribution function by using the particle spectrum extinction equation is an ill-posed integral equation of the first kind [ S. Twomey, J. Comput. Phys. 18, 188 (1975); Y. F. Wang, Computational Methods for Inverse Problems and Their Applications (Higher Education Press, 2007) ], since we are often faced with limited or insufficient observations in remote sensing and the observations are contaminated. To overcome the ill-posed nature of the problem, regularization techniques were developed. However, most of the literature focuses on the application of Phillips–Twomey regularization and its variants, which are unstable in several cases. As is known, the particle size distribution is always nonnegative, and we are often faced with incomplete data. Therefore, we study the active set method and propose a regularizing active set algorithm for ill-posed particle size distribution function retrieval and for enforcing nonnegativity in computation. Our numerical tests are based on synthetic data for theoretical simulations and the field data obtained with a CE 318 Sun photometer for the Po Yang lake region of Jiang Xi Province, China, and are performed to show the efficiency and feasibility of the proposed algorithms.

© 2008 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(010.1100) Atmospheric and oceanic optics : Aerosol detection
(010.1110) Atmospheric and oceanic optics : Aerosols
(100.0100) Image processing : Image processing
(100.3190) Image processing : Inverse problems
(280.1100) Remote sensing and sensors : Aerosol detection

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: September 18, 2007
Revised Manuscript: November 19, 2007
Manuscript Accepted: November 26, 2007
Published: January 14, 2008

Yanfei Wang and Changchun Yang, "Regularizing active set method for retrieval of the atmospheric aerosol particle size distribution function," J. Opt. Soc. Am. A 25, 348-356 (2008)

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